VOL. XXXr.] PHILOSOPHICAL TRANSACTIONS. 543 



that try experiments with that view, to show that the principle, which most 

 of them go upon, is false, and can by no means produce a perpetual motion. 

 They take it for granted, that if a weight descending in a wheel, at a deter- 

 minate distance from the centre, does in its ascent approach nearer to it; such 

 a weight in its descent will always preponderate, and cause an equal weight to 

 rise, provided it comes nearer the centre in its rise; and accordingly as itself 

 rises it will be overbalanced by another equal weight to it; therefore they endea- 

 vour by various contrivances to produce that effect, as if the consequence of it 

 would be a perpetual motion. 



But I shall show, that they mistake one particular case of a general 

 theorem, or rather a corollary of it, for the theorem itself. The theorem is 

 as follows: 



Theor. — If one weight in its descent, does by means of any contrivance, 

 cause another weight to ascend with a less momentum or quantity of motion 

 than itself, it will preponderate and raise the other weight. 



Co7\ 1. — Therefore if the weights be equal, the descending weight must 

 have more velocity than the ascending weight, because the momentum is made 

 up of the weight multiplied into the velocity. 



Cor. 2. — Therefore if a lever or balance, have equal weights fastened or 

 hanging at its ends, and the brachia be ever so little unequal, that weight will 

 preponderate which is farthest from the centre. 



Scholium — This second corollary causes the mistake; because those, who 

 think the velocity of the weight is the line it describes, expect that that weight 

 shall be overpoised which describes the shortest line, and therefore contrive 

 machines to cause the ascending weight to describe a shorter line than the 

 descending weight. As for example, in the circle ADBa, fig. J 7, pi. J 3, the 

 weights A and b being supposed equal, they imagine, that if, by any contrivance 

 whatever, while the weight a describes the arc Aa, the weight b is carried in 

 any arc, as Bb, so as to come nearer the centre in its rising, than if it went up 

 the arc bd; the said weight shall be overpoised, and consequently, by a number 

 of such weights, a perpetual motion will be produced. 



This is attempted by several contrivances, all depending on this false prin- 

 ciple; but I shall only mention one, represented by %. 18, where awheel with 

 two parallel circumferences, has the space between them divided into cells, 

 which being curved, will, when the wheel goes round, cause weights placed 

 loose in the said cells, to descend on the side aaa, at the outer circumference; 

 and on the side d to ascend in the line Bbbb, which comes nearer the centre, 

 and touches the inner circumference. In a machine of this kind, the weights 

 will indeed move in such a manner, if the wheel be turned round, but they 



